Kinestatic Analysis of Multifingered Hands

Abstract

This paper is concerned with the handling of any object by an articulated multifingered hand. By handling we mean the secure grasp of a general object plus the manipulation of this object by the fingers without motion of the arm on which the hand is mounted. Hypothetical joints are used to express the freedom at the contact of the object with each fingertip. A pair of matrices are introduced that relate the small motions of the joints to the relative displacement of the object and the fingertips and that are derived using reciprocal screws. This analysis permits not only the determination of the necessary conditions for a secure handling of the object but also the investigation of the special configurations that may occur. In the case of a grasp with point contact with friction, a very important result is derived that leads to a considerable sim plification in the analysis of these matrices. It is further shown that there exists a particular point, called the center of the grasp, at which the direction of the force applied to the object does not influence the contact intensities. Following this it is demonstrated that the vector containing the contact intensities, generated by a unit couple applied to the object, generates an ellipsoid defined as the grasp ellipsoid. The two smaller axes of this ellipsoid show where to place the con tacts to minimize the contact forces for a given task. The results are illustrated with numeric examples in appendix C.